How to Perform Bootstrapping in R

[This article was first published on Data Science Tutorials, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

The post How to Perform Bootstrapping in R appeared first on Data Science Tutorials

What do you have to lose?. Check out Data Science tutorials here Data Science Tutorials.

How to Perform Bootstrapping in R, Bootstrapping is a method for estimating the standard error of any statistic and generating a confidence interval for the statistic.

The basic bootstrapping procedure is as follows:

Take k repeated replacement samples from a given dataset.

Calculate the statistic of interest for each sample.

These yields k different estimates for a given statistic, which you can then use to calculate the statistic’s standard error and create a confidence interval.

We can perform bootstrapping in R by calling the following boot library functions:

1. Generate bootstrap samples.

boot(data, statistic, R, …)


data: A vector, matrix, or data frame

statistic: A function that produces the statistic(s) to be bootstrapped

R: Number of bootstrap replicates

2. Create a confidence interval using the bootstrap method., conf, type)


bootobject: An object returned by the boot() function

conf: The confidence interval to be computed. The default value is 0.95.

type: The type of confidence interval to compute. Options include “norm”, “basic”, “stud”, “perc”, “bca” and “all” – Default is “all”

The examples below demonstrate how to use these functions in practice.

How to test the significance of a mediation effect (

Bootstrapping a Single Statistic

The code below demonstrates how to compute the standard error for the R-squared of a simple linear regression model:


Now we can define a function to calculate R-squared

rsq_function <- function(formula, data, indices) {
  d <- data[indices,] #allows boot to select sample
  fit <- lm(formula, data=d)

Let’s perform bootstrapping with 3000 replications

reps <- boot(data=mtcars, statistic=rsq_function, R=3000, formula=mpg~disp)

Ready to view the results of bootstrapping

How to Analyze Likert Scale Data? – Data Science Tutorials

boot(data = mtcars, statistic = rsq_function, R = 3000, formula = mpg ~
Bootstrap Statistics :
     original      bias    std. error
t1* 0.7183433 0.003027851  0.06410851

We can see from the results:

This regression model’s estimated R-squared is 0.7183433.

This estimate has a standard error of 0.06513426.

We can also quickly see the distribution of the bootstrapped samples:

Similarity Measure Between Two Populations-Brunner Munzel Test – Data Science Tutorials


We can also use the following code to compute the 95% confidence interval for the model’s estimated R-squared:

Adjusted bootstrap percentile (BCa) interval calculation, type="bca")
Based on 3000 bootstrap replicates
CALL : = reps, type = "bca")
Intervals :
Level       BCa         
95%   ( 0.5474,  0.8160 ) 

We can see from the output that the 95% bootstrapped confidence interval for the true R-squared values is (.5350, .8188).

How to Use Italic Font in R – Data Science Tutorials

The post How to Perform Bootstrapping in R appeared first on Data Science Tutorials

Learn how to expert in the Data Science field with Data Science Tutorials.

To leave a comment for the author, please follow the link and comment on their blog: Data Science Tutorials. offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)